The Analytic Hierarchy Process AHP These slides are mostly taken from Prof. İlker TOPCU s AHP/ANP Lecture notes on http://web.itu.edu.tr/~topcuil/ya/ahp.htm Özgür Kabak, Ph.D.
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Cognitive Psychology has found that people are poor at assimilating large quantities of information on problems People cope with cognitive overload by employing heuristics that simplify the problem This can lead to selection of suboptimal alternatives
George A. Miller, in his paper " The Magical Number Seven, Plus or Minus Two: Some Limits on Our Capacity for Processing Information indicated that the capacity of human short term memory is seven separate items, plus or minus two. The brain of a regular human can simultaneously process, differentiate, and deal with at most 7 factors for some people this limit can be decreased to 5, for some other people it can be increased to 9 (The Psychological Review, 1956, vol. 63, pp. 81-97)
Why Hierarchy? when people faced with a complex problem in order to understand the problem better they must break down the problem into its smaller constituent parts and construct a hierarchical model to represent it
Why Hierarchy? Decision making problem should be depicted as thoroughly as possible: The constructed hierarchy arranging the factors in appropriate levels must include enough relevant detail
Hierarchy Goal Criteria cluster (level) Subcriteria element Alternatives This loop indicates that each element depends only on itself
Supplier Selection Selecting the best material supplier to purchase key components for new products Relationship closeness Quality of product Delivery capabilities Warranty level Average price Reputation Supplier A Supplier B Supplier C
R&D Project Selection Goal Future of the Firm Criteria Technical Marketing Financial Manufacture Sub- Criteria Regulatory Compliance Development Cost Prob. of Tech. Success R&D and Eng. Resources Development Time Patent Position Capability to Market Market Growth Market Share Market Potential Customer Acceptance NPV Capital Invest ROI Unit Cost Capability to Manufacture Facility/Equp. Req. Safety Ratings (for each Sub- Criterion) Outstanding Above Average Average Below Average Outstanding Above Average Average Below Average Outstanding Above Average Average Below Average Outstanding Above Average Average Below Average p1 p2 p99
Whom to marry - a compatible spouse Flexibity Independence Growth Challenge Commitment Humor Intelligence Psychological Physical Socio-cultural Philosophical Aesthetic Communication & Problem Solving Food Sociability World View Housekeeping Family & Children Shelter Finance Theology Sense of Beauty & Intelligence Temper Sex Understanding Security Affection Loyalty Case 1 marry don t marry Case 2 Campbell Graham McGuire Faucet
Sohbetli yaşamın olduğu yer: Bakırköy 1. Huzurlu, güvenli ve refah içinde model bir ilçe oluşturma 2. Sosyal ve kültürel yaşamı iyileştirme ve mozaiğini koruma 3. Ekonomik (hizmet iş kolları) ortamı iyileştirme 4. Fiziksel ortamı (ulaştırma, kent altyapısı) şehir plancılığı yaklaşımıyla iyileştirme 5. Doğal, çevresel ve tarihi güzellikleri koruma 6. Bakırköylülük bilincini geliştirme ve Bakırköy markasını oluşturma 7. Katılımlı, dinamik, çağdaş, sosyal belediyecilik anlayışına uygun bir yerinden yönetim oluşturma 1. Sosyal dokuya yönelik hizmetlerin verilmesi (Kadınlar ve çocuklar için sosyal yaşam evleri; yaşlılar için bakım evleri; engelliler için özel yollar, alış veriş ve hizmet birimleri) 2. Gençlik merkezleri ve mekanları (sanat, kültür, bilişim, hobi ve eğlence) yapılması 3. Nikah salonu yapılması 4. Güzel sanatlar üniversitesi/fakültesi / Sanat akademisi açılmasının teşvik edilmesi 5. Uluslararası düzeyde (dans, müzik, sinema, tiyatro) festivalleri yapılması 6. Kültür ve kongre merkezi kurulması 7. Bakırköy müzesi kurulması 8. Tarihi eserlerin restore edilerek korunması 9. Yeşil alanların, oyun ve spor alanlarının arttırılması 10. Yeşil alanların, oyun ve spor alanalarının arttırılması 11. Ayamama çevresinde botanik bahçesi ve sağlık vadisi oluşturulması 12. Ayamama çevresinde botanik bahçesi ve sağlık vadisi oluşturulması 13. Bütün belediye hizmet birimlerinin toplu halde bulunacağı tek bir bina yapılması 14. Bütün belediye hizmet birimlerinin toplu halde bulunacağı tek bir bina yapılması 15. Özgürlük meydanından kalkan metro ve deniz otobüslerinin entegrasyonu 16. Otoparkların arttırılması ve yeraltı otoparkları kurulması...... 34. Veri tabanı oluşturulması ve iletişim için yararlanılması
Sosyal ortam Eğitim Kültür-Sanat Sağlık Eğlence Spor Yaşanabilir, katılımcı, insan mutluluğuna önem veren bir Eskişehir Ekonomik ortam Fiziki yapı ortamı Doğal ortam Ticaret Hizmet Sanayi Turizm Tarım Yüksek Teknoloji İmar Ulaşım Altyapı Şehir Görüntüsü Hava Toprak Su 1. Toplu Etkinlikler ve Kültür-Sanat Merkezi Projesi 2. Küçük El Sanatları Projesi 3. Spor Projesi 4. Dinlenme Alanları Projesi 5. Bilim ve Teknoloji Parkı / Mesleki Eğitim Projesi Dış ortam (Entegrasyon) Bölgesel Ulusal Uluslararası Katılım ortamı Yerel Yönetim Merkezi Yönetim Sivil Toplum Kuruluşları Özel Sektör
Sektör içi işbirliği Yerli birleşme Ortak tanıtım(iç/dış) Sektör içi eğitimve kurumsallaşma İhracatta işbirliği Sözleşmeli AR-GE Co-marketing, Co-promotion Uluslararası ölçüde rekabet gücüne sahip, yaşam kalitesini arttırıcı ve ülke ihtiyacının büyük kısmını karşılayan ilaç sanayinin bulunması İth.- ihr. dengesi Ar-Ge ve yenilikçilik Hammadde üretimi Fon yaratılması Tüketici bilinci Devletle işbirliği Dağ. kanallarıyla işb. Üniversitelerle işb. Yönlendirici devlet (yerli hammadde, Ar-Ge ye teşvik, Üretim yatırımına (yab.ser.) teşvik, AB ye uyu, Bioeşdeğerlilik) Yeni Mevzuat (Geri Ödeme Sistemi, OTC Yönetmeliği, KDV'nin düşmesi, KKDF'nin kalkması, İDY, Fiyat kararnamesi) Fiyatın piy.tar. belirlenmesi Bağımsız ilaç otoritesi Sosyal güvenlik reformunun genişletilmesi Dağıtım kanallarında kurumsallaşma Dağıtım kanallarında eğitim AR-GE Eğitim Üretimin sürekliliği Hekimlerle işbirliği Etik kuralların uygulanması Eğitimle reçetelemenin iyileştirilmesi Hekimin hastayla para ilişkisinin bitmesi Eczanelerle işbirliği Eczanelerarası network Eczacıların danışmanlık hizmeti
İhtiyacı karşılamak için sisteme karşı güven oluşturarak kadavra donör sayısını arttırmak 1. Beyin ölümü tespit ve bildirim sürecini iyileştirme 2. Yoğun bakım standartlarını iyileştirme 3. Yasal boşlukları giderme (yasa, yönetmelik) 4. Organ nakli koordinasyon sistemini iyileştirme 5. Organ nakli ekonomisini güçlendirme 6. Sağlık hizmet zincirinin tüm halkalarını bilgilendirmebilinçlendirme 7. Toplumsal iletişimi etkinleştirme 1. Organ nakli merkezlerinin oluşturulması (dedike merkezlerin belirlenmesi ve sayının sınırlanması) 2. Organ bandrolü uygulamasının başlatılması 3. Ülkenin tüm kurumlarının kabul ettiği düzenleyici kurul/ üst kurul kurulması (bilimsel, dinamik, siyasetten bağımsız, devlete yakın, karar veren, hesap soran bir Profesyonel Transplantasyon Organizasyon kurulu, ulusal/bölgesel) 4. Donör bildirimi sonrasında ameliyat hastanesinin belirlenme mekanizmasının oluşturulması, sistematiğin belirlenmesi 5. Beyin ölümü sonrası organizasyonun düzenlenmesi, yoğun bakıma yönelik beyin ölümü tanımı sonrası donör bakım eğitimlerinin verilmesi 6. Beyin ölümü yasal karar sisteminin düzenlenmesi, yönetmelik çıkarılması 7. Beyin ölümü- Sigorta (Kamu-Özel Sektör) ilişkisinin düzenlenmesi 8. Yoğun bakım standartlarının belirlenmesi için yönetmeliğin hazırlanması ve bir an önce çıkarılması...... 25. Organ naklinde tek adres, tek telefon sistemi/ Alo Sağlık 184 telefon hattı bu konuda test edilmesi
The Analytic Hierarchy Process is a powerful and understandable methodology that allows groups or individuals to combine qualitative and quantitative factors in decision making process. a Multi Criteria Decision Making method for complicated and unstructured problems. an approach that uses a hierarchical model having levels of goal, criteria, possible sub-criteria, and alternatives.
Priorities: Importance - Preference AHP captures priorities from paired comparison judgments of the elements of the decision with respect to each of their parent criteria: Paired comparison judgments are arranged in a matrix Priorities are derived from the matrix as its principal eigenvector It also allows for the measurement of inconsistency in judgment
Importance of elements are equal Decision maker is indifferent between elements 9 8 7 6 5 4 3 2 1
First element is moderately more important than second one First element is moderately preferred to second one 9 8 7 6 5 4 3 2 1
First element is strongly more important than second one First element is strongly preferred to second one 9 8 7 6 5 4 3 2 1
First element is very strongly more important than second one First element is very strongly preferred to second one 9 8 7 6 5 4 3 2 1
First element is extremely more important than second one First element is strongly preferred to second one 9 8 7 6 5 4 3 2 1
Intermediate values 9 8 7 6 5 4 3 2 1
Use reciprocals for inverse comparisons 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9
Supplier Selection Selecting the best material supplier to purchase key components for new products Relationship closeness Quality of product Delivery capabilities Warranty level Average price Reputation Supplier A Supplier B Supplier C
Relationship closeness Quality of product Delivery capabilities Warranty level Average price Reputation Comparison of criteria w.r.t. goal Priorities Relationship closeness Quality of product Delivery capabilities Warranty level Average price Reputation
Relationship closeness Quality of product Delivery capabilities Warranty level Average price Reputation Comparison of criteria w.r.t. goal Priorities Relationship closeness 1 Quality of product 1 Delivery capabilities 1 Warranty level 1 Average price 1 Reputation 1
Relationship closeness Quality of product Delivery capabilities Warranty level Average price Reputation Comparison of criteria w.r.t. goal Priorities Relationship closeness 1 Moderately - strongly Quality of product 1 Delivery capabilities 1 Warranty level 1 Average price 1 Reputation 1
Relationship closeness Quality of product Delivery capabilities Warranty level Average price Reputation Comparison of criteria w.r.t. goal Priorities Relationship closeness 1 4 Quality of product 1 Delivery capabilities 1 Warranty level 1 Average price 1 Reputation 1
Relationship closeness Quality of product Delivery capabilities Warranty level Average price Reputation Comparison of criteria w.r.t. goal Priorities Relationship closeness 1 4 Quality of product 1 Very strongly Delivery capabilities 1 2.nd element strongly Warranty level 1 Equal Average price 1 Moderately Reputation 1
Relationship closeness Quality of product Delivery capabilities Warranty level Average price Reputation Comparison of criteria w.r.t. goal Priorities Relationship closeness 1 4 Quality of product 1 7 Delivery capabilities 1 1/5 Warranty level 1 1 Average price 1 3 Reputation 1
Relationship closeness Quality of product Delivery capabilities Warranty level Average price Reputation Comparison of criteria w.r.t. goal Priorities Relationship closeness 1 4 3 1 3 4 Quality of product 1 7 3 1/5 1 Delivery capabilities 1 1/5 1/5 1/6 Warranty level 1 1 1/3 Average price 1 3 Reputation 1
Relationship closeness Quality of product Delivery capabilities Warranty level Average price Reputation Comparison of criteria w.r.t. goal Priorities Relationship closeness 1 4 3 1 3 4 Quality of product 1/4 1 7 3 1/5 1 Delivery capabilities 1/3 1/7 1 1/5 1/5 1/6 Warranty level 1 1/3 5 1 1 1/3 Average price 1/3 5 5 1 1 3 Reputation 1/4 1 6 3 1/3 1
Relationship closeness Quality of product Delivery capabilities Warranty level Average price Reputation Comparison of criteria w.r.t. goal Priorities Relationship closeness 1 4 3 1 3 4.32 Quality of product 1/4 1 7 3 1/5 1.14 Delivery capabilities 1/3 1/7 1 1/5 1/5 1/6.03 Warranty level 1 1/3 5 1 1 1/3.13 Average price 1/3 5 5 1 1 3.24 Reputation 4 1 6 3 1/3 1.14
Comparison of suppliers w.r.t. criteria Relationship closeness A B C Priorities A 1 1/3 1/2.16 B 3 1 3.59 C 2 1/3 1.25 Quality of product A B C Priorities A 1 1 1.33 B 1 1 1.33 C 1 1 1.33 Delivery capabilities A B C Priorities A 1 5 1.45 B 1/5 1 1/5.09 C 1 5 1.46 Warranty level Average price Reputation A B C Priorities Prices $ Priorities A B C Priorities A 1 9 7.77 B 1/9 1 1/5.05 C 1/7 5 1.17 A 10.25 B 5.50 C 10.25 A 1 6 4.69 B 1/6 1 1/3.09 C 1/4 3 1.22
Composition and synthesis Impact of suppliers on goal +
Relationship closeness Quality of product Delivery capabilities Warranty level Average price Reputation Composition and synthesis Impact of suppliers on goal Composite impact of suppliers.32.14.03.13.24.14 A B C
Composition and synthesis Impact of suppliers on goal +
Relationship closeness Quality of product Delivery capabilities Warranty level Average price Reputation Composition and synthesis Impact of suppliers on goal Composite impact of suppliers.32.14.03.13.24.14 A.16.33.45.77.25.69 B.59.33.09.05.50.09 C.25.33.46.17.25.22
Relationship closeness Quality of product Delivery capabilities Warranty level Average price Reputation Composition and synthesis Impact of suppliers on goal Composite impact of suppliers.32.14.03.13.24.14 A.16.33.45.77.25.69.37 B.59.33.09.05.50.09 C.25.33.46.17.25.22
Relationship closeness Quality of product Delivery capabilities Warranty level Average price Reputation Composition and synthesis Impact of suppliers on goal Composite impact of suppliers.32.14.03.13.24.14 A.16.33.45.77.25.69.37 B.59.33.09.05.50.09.38 C.25.33.46.17.25.22.25
Eigenvector solution A a b c a 1 0.5 3 b 2 1 4 c 0.33 0.25 1 Sum 3.33 1.75 8.00 Column normalization x/sum a b c a 0.3 0.286 0.38 b 0.6 0.571 0.50 c 0.1 0.143 0.13 1 1 1 w 0.3202 0.5571 0.1226 Row average
Normalisation when scores of the alternatives are know Prices $ A 10 B 5 Get the inverse for cost attributes 1/price A 1/10 B 1/5 Normalise w.r.t. sum of the column Priorities A 0.25 B 0.5 C 10 C 1/10 C 0.25 Number of deliveries on time # A 8 B 7 C 5 sum 0.4 # A 8 B 7 C 5 sum 20 Priorities A 0.4 B 0.35 C 0.25
Consistency w.3202.5571.1226 Aw 0.97 1.69 0.37 Aw w 3.0186 3.0300 3.0065 average 3.0183 λ max n RI 3 0.52 4 0.89 5 1.11 6 1.25 7 1.35 8 1.40 9 1.45 CI= RI= λ max - n n - 1 Consistency index SEE TABLE =0.0092 =0.52 Random consistency index CR = CI RI Consistency ratio =1.76%
Relationshi p closeness Quality of product Delivery capabilities Warranty level Average price Reputation Relationshi p closeness Quality of product Delivery capabilities Warranty level Average price Reputation Group Decision Making Sourcing Manager: Relationship closeness is strongly more important than Quality of product Production Manager: Quality of product is strongly more important than Relationship closeness Prioriti es Prioriti es Relations hip closeness Quality of product Delivery capabiliti es 1 5 1 1 Relations hip closeness Quality of product Delivery capabiliti es 1 1/5 1 1 Warranty level 1 Warranty level 1 Average price 1 Average price 1 Reputatio n 1 Reputatio n 1
Relationshi p closeness Quality of product Relationshi p closeness Quality of product Relationshi p closeness Quality of product Group Decision Making Sourcing Manager: Relationship closeness is strongly more important than Quality of product Production Manager: Quality of product is strongly more important than Relationship closeness Relations hip closeness Quality of product 1 5 1 Combined Decision? Relations hip closeness Quality of product 1 1/5 1 Relations hip closeness Quality of product 1? 1/? 1
Group Decision Making A B DM1 very strongly (7) A 1 X B 1/X 1 DM2 moderately (3) Use arithmetic mean to combine decisions? X = (7+3)/2 = 5 1/X = (1/7+1/3)/2 = 0.24 1/5 Use geometric mean to combine decisions? X = (7*3) = 4.58 1/X = (1/7*1/3) = 0.22 = 1/4.58
Group Decision Making DM1 DM2 a b c a b c a 1 0.5 3 a 1 1 0.25 b 2 1 4 b 1 1 3 c 0.33 0.25 1 c 4 0.33 1 Combine preferences DM1&DM2 a b c a 1 0.707 0.866 b 1.414 1 3.464 c 1.155 0.289 1
AHP Rating Evaluating Employees for Raises Criteria Dependability Education Experience Attitude Leadership w 15.50% 24.00% 13.80% 17.20% 29.50% rating intensities Dependability Outstanding.48 1 Very good.28.58 Good.16.33 Average.05.10 Unsatisfactory.03.06
AHP Rating Evaluating Employees for Raises Criteria Dependability Education Experience Attitude Leadership w 15.50% 24.00% 13.80% 17.20% 29.50% rating intensities Education Doctorate.59 1 Masters.25.42 Bachelors.11.19 High school.05.08
AHP Rating Evaluating Employees for Raises Criteria Dependability Education Experience Attitude Leadership w 15.50% 24.00% 13.80% 17.20% 29.50% rating intensities Experience > 15 years.61 1 6 15 years.25.41 3 5 years.10.16 < 3 years.04.07
AHP Rating Evaluating Employees for Raises Criteria Dependability Education Experience Attitude Leadership w 15.50% 24.00% 13.80% 17.20% 29.50% rating intensities Attitude Enthused.49 1 Very good.26.53 Good.14.29 Average.08.16 Bad.03.06
AHP Rating Evaluating Employees for Raises Criteria Dependability Education Experience Attitude Leadership w 15.50% 24.00% 13.80% 17.20% 29.50% rating intensities Leadership Good.66 1 Average.29.44 Bad.05.08
Candidate Dependability 15.50% AHP Rating Evaluating Employees for Raises Education 24.00% Experience 13.80% Attitude 17.20% Leadership 29.50% 1 Outstanding Doctorate > 15 years Enthused Good 2 Average Masters < 3 years Enthused Good 3 Good Bachelors > 15 years Very good Bad 4 Good Masters 3-5 years Very good Good 5 Average Bachelors 3 5 years Good Average 6 Outstanding Masters < 3 years Very good Average 7 Outstanding Bachelors 6 15 years Good Average 8 Very good Masters 6 15 years Average Good 9 Outstanding Masters 3 5 years Very good Average 10 Very good Doctorate 6 15 years Good Average 11 Unsatisfactory Bachelors 6 15 years Good Average 12 Very good Bachelors 3 5 years Enthused Good 13 Good Doctorate > 15 years Enthused Good 14 Good High school 3 5 years Very good Average 15 Outstanding Doctorate < 3 years Very good Average
Candidate Dependability 15.50% AHP Rating Evaluating Employees for Raises Education 24.00% Experience 13.80% Attitude 17.20% Leadership 29.50% Total Points 1 1 1 1 1 1 1 2.10.42.07 1 1.59 3.33.19 1.53.08.35 4.33.42.16.53 1.56 5.10.19.16.29.44.26 6 1.42.07.53.44.49 7 1.19.41.29.44.44 8.58.42.41.16 1.57 9 1.42.16.53.44.50 10.58 1.41.29.44.57 11.06.19.41.29.44.29 12.58.19.16 1 1.62 13.33 1 1 1 1.90 14.33.08.16.53.44.32 15 1 1.07.53.44.62
AHP Rating Evaluating Employees for Raises Candidate Total Points 1 1 13.90 12, 15.62 2.59 8, 10.57 4.56 9.50 6.49 7.44 3.35 14.32 11.29 5.26
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Next Class Tomorrow!! Topic: Location Strategy